The rank of a graph 
is defined as 
,
where 
is the number of vertices on 
and 
is the number of connected components (Biggs 1993, p. 25).
Graph Rank
See also
Graph Co-Rank, Rank PolynomialExplore with Wolfram|Alpha
References
Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, p. 25, 1993.Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, 2001.Referenced on Wolfram|Alpha
Graph RankCite this as:
Weisstein, Eric W. "Graph Rank." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GraphRank.html